Estimation of the Average Treatment Effect (ATE) is often carried out in 2 steps, wherein the first step, the treatment and outcome are modeled, and in the second step the predictions are inserted into the ATE estimator. In the first steps, numerous models can be fit to the treatment and outcome, including using machine learning algorithms. However, it is a difficult task to choose among the hyperparameter sets which will result in the best causal effect estimation and inference. Multiply Robust (MR) estimator allows us to leverage all the first-step models in a single estimator. We show that MR estimator is $n^r$ consistent if one of the first-step treatment or outcome models is $n^r$ consistent. We also show that MR is the solution to a broad class of estimating equations, and is asymptotically normal if one of the treatment models is $\sqrt{n}$-consistent. The standard error of MR is also calculated which does not require a knowledge of the true models in the first step. Our simulations study supports the theoretical findings.

翻译：平均处理效应（ATE）的估计通常分两步进行：第一步对处理变量和结果变量建模，第二步将预测值代入ATE估计器。在第一步中，可以使用包括机器学习算法在内的多种模型拟合处理变量和结果变量。然而，从众多超参数组合中选择能产生最佳因果效应估计和推断的集合是一项艰巨任务。多稳健（MR）估计器允许我们在单一估计器中利用所有第一步的模型。我们证明：若第一步的处理模型或结果模型中至少有一个具有$n^r$一致性，则MR估计器具有$n^r$一致性；同时表明MR估计器是某类广义估计方程的解，且当其中一个处理模型具有$\sqrt{n}$一致性时，该估计量渐近正态。我们还计算了MR估计器的标准误差，该计算无需知晓第一步的真实模型。仿真研究验证了理论推导的有效性。